Question

1. solve the equation below.

\sqrt{6y + 15} - 4 = y

Explanation:

Step1: Isolate the square root term

$\sqrt{6y+15} = y + 4$

Step2: Square both sides

$(\sqrt{6y+15})^2 = (y + 4)^2$
$6y + 15 = y^2 + 8y + 16$

Step3: Rearrange to quadratic form

$y^2 + 8y + 16 - 6y - 15 = 0$
$y^2 + 2y + 1 = 0$

Step4: Factor the quadratic

$(y + 1)^2 = 0$

Step5: Solve for y and verify

$y = -1$
Substitute back: $\sqrt{6(-1)+15}-4 = \sqrt{9}-4 = 3-4 = -1$, which matches y.

Answer:

$y = -1$